High-concurrency tri-mode memristor-based ordinary differential equation solver.

Abstract

Ordinary differential equations (ODEs) are widely used in science, engineering, and mathematics, but their numerical solution on traditional Von Neumann hardware is time- and energy-consuming, especially for high-order ODEs. Here, we present a high-concurrency memristor-based ODE solver supporting arbitrary order and three configurable modes: coarse, fine, and coarse-to-fine look-ahead, to meet diverse accuracy requirements. History-based memristor programming (HMP) accelerates device conductance programming by up to 3.29 × without compromising accuracy. The reconfigurable hardware implements coarse solver via analog compute-in-memory, fine solver via digital compute-in-memory, and coarse-to-fine solver using Parareal methods for high-concurrency numerical integration. We demonstrate its performance on exponential functions, Lorenz attractors, and three-body problems, achieving 601 × ~ 6.92 × 10³ × speedup and 1.71 × 10³ × ~ 3.93 × 10³ × energy improvement over CPU/GPU, respectively, when solving the same ODE tasks. The memristor-based tri-mode solver pushes ODE solver hardware performance to a new paradigm with orders of magnitude concurrency improvements.